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Suppose a normal distribution has a mean of 62 and a standard deviation of4. What is the probability that a data value is between 57 and 65? Round youranswer to the nearest tenth of a percent.

Suppose A Normal Distribution Has A Mean Of 62 And A Standard Deviation Of4 What Is The Probability That A Data Value Is Between 57 And 65 Round Youranswer To T class=

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SOLUTION

From the given data the mean is 62 and standard deviation is 4

It is required to find the probability that a data value is between 57 and 62

That is:

[tex]P(57\lt x\lt65)[/tex]

The z scores is calculated using:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using the x values it follows:

[tex]z=\frac{57-62}{4}=-1.25[/tex]

Also,

[tex]z=\frac{65-62}{4}=0.75[/tex]

Thus the required probability is:

[tex]P(-1.25The proability is:[tex]P(-1.25This can be expressed as percentage as:[tex]P(-1.25\lt z\lt0.75)=66.8\%[/tex]

Therefore the correct option is C

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